PARIS—Directors of French pharmaceutical giant Sanofi SA heard reports earlier this year that took them by surprise: the company’s chief executive, Christopher Viehbacher, was considering selling or splitting off a portfolio of older drugs valued at more than $8 billion.

Alarmed, some directors asked Chairman Serge Weinberg to confront Mr. Viehbacher, according to a person familiar with the matter. Mr. Weinberg “talked to Chris. He...